Analysis Of Laminar Natural Convection Research Articles

Patterned convection in inclined slots

An analysis of laminar natural convection in inclined slots subjected to patterned heating has been performed. The imposed heating takes a simple form characterized by a single Fourier mode combined with uniform heating. It is shown that periodic heating applied at the lower plate produces no net flow when the slot is either horizontal or vertical, but a net upward flow is generated when the slot is tilted. Periodic heating applied at the upper plate produces net downward flow in the inclined situation. The addition of uniform heating promotes the upward flow while cooling has the opposite effect. There is a critical inclination angle at which the maximum net flow rate is greatest. Dynamic and thermal boundary layers are present when the wavenumber of the imposed heating is large. The use of heating at both plates, with the same wavenumber, leads to a flow dominated by the plate exposed to a more intense heating; when the two plates are heated equally no net flow is observed irrespective of the inclination angle. Changes of the relative positions of the two patterns can change the net flow rate by up to 50 %. The intensity of the flow increases with reduction of the Prandtl number. If the heating applied to the plates is of different wavelength, but of the same intensity, a wide range of behaviours of the flow system is possible. The details of this response are sensitive to the ratio of the two wavenumbers.

LAMINAR NATURAL CONVECTIVE HEAT TRANSFER IN PARABOLIC ENCLOSURES

A finite volume analysis of laminar natural convection of air within full parabolic enclosures heated from below is reported for the enclosure aspect ratio 0.27 £ AR £ 0.7 and a range of the Rayleigh number 5.5 x 106 £ Ra £ 9.8 x 107. The shape of the enclosures strongly affects the results obtained. Quasi-symmetrically arranged counter-rotating vortices are formed in each of the enclosures. The shape of the cells are influenced by the bounding curved and flat surfaces as they change from being rectangular at the periphery to circular at the core. There are reduction in the size and intensity of the on the cells from the center to the bottom corners. At steady state, there exists in each enclosure a central thermal plume that thickens as the roof pitch angle increases. The heat transfer pattern matches the flow of the plumes and jets from the walls. For the 15o roof pitch enclosure, the heat transfer rate increases sharply at a critical Ra value of 5 x 106.

Entropy generation due to natural convection of a nanofluid in a partially open triangular cavity

A numerical analysis of laminar natural convection with entropy generation in a partially heated open triangular cavity filled with a Cu-water nanofluid has been carried out. Mathematical model including partial differential equations and boundary conditions has been solved by using finite difference method. Particular efforts have been focused on the effects of Rayleigh number, nanoparticles volume fraction and position of the local heater on streamlines, isotherms, local entropy generation as well as local and average Nusselt number, average Bejan number, average entropy generation and fluid flow rate. Obtained results have demonstrated that the heat transfer enhancement and fluid flow attenuation with nanoparticles volume fraction, mainly for high values of Rayleigh number.

Effective utilization of MWCNT–water nanofluid for the enhancement of laminar natural convection inside the open square enclosure

A finite difference based two dimensional numerical analysis of laminar natural convection inside the open square enclosure containing nanofluid of water with multi-walled carbon nanotube (MWCNT) is presented by stream function–vorticity approach. The left wall is subjected to sinusoidal time-variant temperature. The top and bottom walls are considered as adiabatic and the right wall is kept as ambient. The flow is diagonally downward and opposed by the buoyancy force. In the numerical analysis, Xue [30] model of thermal conductivity is coupled with modified Krieger and Dougherty (K–D) model of viscosity based on rheology of suspension of particles. The variables considered in the present study are Rayleigh number (104–106), volumetric fraction of MWCNT (0<ϕ<1.5%), amplitude (0<a<0.5) and the period (τ=0.2). The periodic results of fluid flow are elucidated with streamlines, isotherms and time averaged Nusselt number. The heat transfer intensifies when both the Rayleigh number and percentage of MWCNT increases. The effect of amplitude on the rate of heat transfer is remarkable on the hot wall but is subtle on the opposite cold wall.

Effect of the buoyancy force on natural convection in a cubical cavity with a heat source of triangular cross-section

Numerical analysis of laminar natural convection inside a cubical cavity with a local heat source of triangular cross-section has been conducted. The mathematical model formulated in dimensionless variables such as "vector potential functions - vorticity vector" has been solved by the finite difference method of the second order accuracy. The three-dimensional temperature fields, 2D streamlines and isotherms in a wide range of the Rayleigh number from 104 to 106 have been presented illustrating variations of the fluid flow and heat transfer.

Analysis of natural convection in tall vertical cavities heated by a linear heat flux and cooled isothermally

Purpose – This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues. Design/methodology/approach – The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm. Findings – The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ=0, 1 and −1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra m (103Ra m 3×104) and the aspect ratio A (10A80). It was found that for a given A and Ra m , the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters. Practical implications – Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ=−1. Originality/value – Despite its fundamental and practical interest, natural convection in cavities with 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.

Numerical Analysis of Laminar Natural Convection in a Quadrantal Cavity with a Solid Adiabatic Fin Attached to the Hot Vertical Wall

Numerical Analysis of Laminar Natural Convection in a Quadrantal Cavity with a Solid Adiabatic Fin Attached to the Hot Vertical Wall

Natural convection in a triangular enclosure due to non-uniform cooling on top

Natural convection in a triangular enclosure subject to non-uniform cooling at the inclined surfaces and uniform heating at the base is investigated numerically. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using the Finite Volume Method. Since the upper surface is cooled and the bottom surface is heated, the air flow in the enclosure is potentially unstable to Rayleigh--Benard instability. Based on the numerical results, the transient flow development in the enclosure is classified into three distinct stages: an early stage, a transitional stage, and a steady stage. In addition, the flow inside the enclosure strongly depends on the governing parameters; Rayleigh number and aspect ratio. The asymmetric behaviour of the flow about the geometric centre line is discussed in detailed. The heat transfer through the roof and the ceiling as a form of Nusselt number is also reported. References O. M. Kamiyo, D. Angeli, G. S. Barozzi, M. W. Collins, V. O. S. Olunloyo, S. O. Talabi, A comprehensive review of natural convection in triangular enclosures, Applied Mechanics Reviews , 63 , 060801. doi:10.1115/1.4004290 S. C. Saha, M. M. K. Khan, A review of natural convection and heat transfer in attic-shaped space, Energy and Buildings , 43 , 2564--2571. doi:10.1016/j.enbuild.2011.06.020 V. A. Akinsete, T. A. Coleman, Heat transfer by steady laminar free convection in triangular enclosures, Int. J. Heat Mass Trans. , 25 , 1982, 991--998. doi:10.1016/0017-9310(82)90074-6 E. M. del Campo, M. Sen, E. Ramos, Analysis of laminar natural convection in a triangular enclosure, Numer. Heat Transfer , 13 , 1988, 353--372. doi:10.1080/10407788808913618 H. Asan, L. Namli, Numerical simulation of buoyant flow in a roof of triangular cross-section under winter day boundary conditions, Energy and Buildings 33 , 2001, 753--757. doi:10.1016/S0378-7788(01)00063-9 D. Poulikakos, A. Bejan, The fluid dynamics of an attic space, J. Fluid Mech. 131 , 1983, 251--269. doi:10.1017/S0022112083001317 C. Lei, S. W. Armfield, J. C. Patterson, Unsteady natural convection in a water-filled isosceles triangular enclosure heated from below, Int. J. Heat Mass Trans. 51 , 2008, 2637--2650. doi:10.1016/j.ijheatmasstransfer.2007.09.036 S. C. Saha, J. C. Patterson, C. Lei, Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions, Heat Mass Transfer , 46 , 2010, 1432--1181. doi:10.1007/s00231-010-0607-5 S. C. Saha, Unsteady natural convection in a triangular enclosure under isothermal heating, Energy and Buildings , 43 , 2011a, 695-703. doi:10.1016/j.enbuild.2010.11.014 S. C. Saha, Scaling of free convection heat transfer in a triangular cavity for $Pr > 1$, Energy and Buildings , 43 , 2011b, 2908--2917. doi:10.1016/j.enbuild.2011.07.016 G. A. Holtzman, R. W. Hill, K. S. Bal, Laminar natural convection in isosceles triangular enclosures heated from below and symmetrically cooled from above, J. Heat Transfer , 122 , 2000, 485--491. doi:10.1115/1.1288707 S. C. Saha, J. C. Patterson, C. Lei, Natural convection and heat transfer in attics subject to periodic thermal forcing, Int. J. Thermal Sciences , 49 , 2010, 1899--1910. doi:10.1016/j.ijthermalsci.2010.05.010

Numerical Analysis of Laminar Natural Convection in Square Enclosure with and without Partitions and Study Effect of pPartition on the Flow Pattern and Heat Transfer

Numerical Analysis of Laminar Natural Convection in Square Enclosure with and without Partitions and Study Effect of pPartition on the Flow Pattern and Heat Transfer

Numerical analysis of laminar natural convection in isosceles triangular enclosures

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

Numerical analysis of laminar natural convection in isosceles triangular enclosures for cold base and hot inclined walls

In this work, a numerical analysis of laminar natural convection in an enclosure of isosceles triangular cross-section has been performed for cold base and hot inclined walls. Base angles varying from 15° to 75° have been used for different Rayleigh numbers ranging from 10 3 to 10 5. Effects of Rayleigh number and aspect ratio on the flow field and heat transfer are analyzed. The streamline patterns and temperature distributions are presented. It is observed that the enclosures with a low aspect ratio have higher heat transfer rates from the bottom surface of the triangular enclosure.

Natural convection adjacent to a sidewall with three fins in a differentially heated cavity

Natural convection in a differentially heated cavity with three fins on a sidewall is numerically investigated. Due to the presence of the fins, separation of the thermal flows around the fins occurs, and the thermal flows separating from the fins oscillate. The oscillations of the thermal flows around the fins improve the convection flows adjacent to the finned sidewall, and the heat transfer through the finned sidewall is significantly enhanced (by up to 33% at the early stage). This flow configuration is of practical significance for many industrial systems. References S. V. Patankar, Numerical heat transfer and fluid flow, Hemisphere Publishing Corp., 1980 R. Scozia and R. L. Frederick, Natural convection in slender cavities with multiple fins attached on an active wall, Numer. Heat Transfer Part A 20, 127--158, 1991. F. Xu, J. C. Patterson and C. Lei, Oscillations induced by a thin fin on the sidewall of a differentially heated cavity, Proc. 13th International Heat Transfer Conference, Sydney, 2006. F. Xu, J. C. Patterson and C. Lei, Experimental observations of the thermal flow around a square obstruction on a vertical wall in a differentially heated cavity, Exp. Fluids, 40, 364--371, 2006. doi:10.1007/s00348-005-0073-x N. Yucel and H. Turkoglu, Numerical analysis of laminar natural convection in enclosures with fins attached to an active wall, Heat and Mass Transfer, 33, 307--314, 1998. E. Bilgen, Natural convection in cavities with a thin fin on the hot wall, Int. J. Heat Mass Transfer, 48, 3493--3505, 2005. doi:10.1016/j.ijheatmasstransfer.2005.03.016 G. N. Facas, Natural convection in a cavity with fins attached to both vertical walls, J. Thermophys. Heat Transfer, 7, 555--560, 1993. E. K. Lakhal, M. Hasnaoui, E. Bilgen, and P. Vasseur, Natural convectin in inclined rectangular enclosures with perfectly conducting fins attached on the heated wall, Heat Mass Transfer, 32, 365--373, 1997. J. C. Patterson and S. W. Armfield, Transient features of natural convection in a cavity, J. Fluid Mech., 219, 469--497, 1990. doi:10.1017/S0022112090003032

Numerical analysis of laminar natural convection in enclosures with fins attached to an active wall

Vertical enclosures with conducting fins attached to the cold wall were considered. Side walls were kept at constant but different temperatures, while horizontal top and bottom walls were insulated. A conjugate formulation was used for the mathematical formulation of the problem, and a computer program based on the control volume approach and the SIMPLE algorithm was developed. Computations were performed to investigate the effects of the fin configuration and Rayleigh number on the flow structure and heat transfer. It was observed that the heat transfer rate through an enclosure can be controlled by attaching fins to the wall(s) of the enclosure. At low Rayleigh numbers (conduction controlled regime), the heat transfer rate increases with the increasing number of fins and the fin length. However, at higher Rayleigh numbers (convection dominant regimes), the heat transfer rate can be decreased or increased by properly choosing the number of fins and the fin lengths.

Analysis of Laminar Natural Convection in a Triangular Enclosure

Analysis of Laminar Natural Convection in a Triangular Enclosure

Finite-Element Analysis of Laminar Natural Convection in Confined Rectangular Regimes—Extrapolation to Zero Element Size

Finite-Element Analysis of Laminar Natural Convection in Confined Rectangular Regimes—Extrapolation to Zero Element Size

Numerical Analysis of Laminar Natural Convection Between Concentric and Eccentric Cylinders

Numerical Analysis of Laminar Natural Convection Between Concentric and Eccentric Cylinders

Erratum: “Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below” (Journal of Heat Transfer, 1976, 98, pp. 202–207)

Erratum: “Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below” (Journal of Heat Transfer, 1976, 98, pp. 202–207)

Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below

An improved model and algorithm were developed for the numerical solution of three-dimensional, laminar natural convection in enclosures. Illustrative calculations were carried out for heating from below in a cubical box, a long channel with a square cross section and in the region between infinite, horizontal plates. The results are in good agreement with prior experimental and theoretical results. For the infinite flat plates the three-dimensional model correctly produces a two-dimensional solution. For the cube the solution produces different stable solutions depending on the initial conditions. A fluid-particle path is shown to be a good method of illustrating the three-dimensional motion. In the cube and in each cubical cell in the channel this streak-line was found to consist of a pair of double helices.